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Recommendations for using Simulated Annealing in task mapping

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Abstract

A Multiprocessor System-on-Chip (MPSoC) may contain hundreds of processing elements (PEs) and thousands of tasks but design productivity is lagging the evolution of HW platforms. One problem is application task mapping, which tries to find a placement of tasks onto PEs which optimizes several criteria such as application runtime, intertask communication, memory usage, energy consumption, real-time constraints, as well as area in case that PE selection or buffer sizing are combined with the mapping procedure. Among optimization algorithms for the task mapping, we focus in this paper on Simulated Annealing (SA) heuristics. We present a literature survey and 5 general recommendations for reporting heuristics that should allow disciplined comparisons and reproduction by other researchers. Most importantly, we present our findings about SA parameter selection and 7 guidelines for obtaining a good trade-off made between solution quality and algorithm’s execution time. Notably, SA is compared against global optimum. Thorough experiments were performed with 2–8 PEs, 11–32 tasks, 10 graphs per system, and 1000 independent runs, totaling over 500 CPU days of computation. Results show that SA offers 4–6 orders of magnitude reduction is optimization time compared to brute force while achieving high quality solutions. In fact, the globally optimum solution was achieved with a 1.6—90 % probability when problem size is around 1e9–4e9 possibilities. There is approx. 90 % probability for finding a solution that is at most 18 % worse than optimum.

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Authors and Affiliations

  1. Tampere University of Technology, Tampere, Finland

    Heikki Orsila, Erno Salminen & Timo Hämäläinen

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  1. Heikki Orsila
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  2. Erno Salminen
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  3. Timo Hämäläinen
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Correspondence to Heikki Orsila.

Appendix: Convergence results to larger systems with 3–6 PEs

Appendix: Convergence results to larger systems with 3–6 PEs

Table 13 Proportion of SA+AT runs that converged within p from global optimum for 3 PEs and 21 nodes. A higher value is better. SA+AT chooses L=42. The 90 % level is marked in boldface on each column
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Table 14 Approximate expected number of mappings for SA+AT with 3 PEs and 21 nodes. SA+AT chooses L=42. The best values (smallest) are in boldface for each performance level p (row)
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Table 15 Proportion of SA+AT runs that converged within p from global optimum for 4 PEs and 17 nodes. A higher value is better. SA+AT chooses L=51
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Table 16 Approximate expected number of mappings for SA+AT with 4 PEs and 17 nodes. SA+AT chooses L=51
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Table 17 Proportion of SA+AT runs that converged within p from global optimum for 6 PEs and 13 nodes. A higher value is better. SA+AT chooses L=65
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Table 18 Approximate expected number of mappings for SA+AT with 6 PEs and 13 nodes. SA+AT chooses L=65
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Orsila, H., Salminen, E. & Hämäläinen, T. Recommendations for using Simulated Annealing in task mapping. Des Autom Embed Syst 17, 53–85 (2013). https://doi.org/10.1007/s10617-013-9119-0

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